1. Design a BCD-to-decimal decoder using the unused combinations
of the BCD code as don't-care conditions.

2. Implement a full-adder with two 4 X 1 multiplexers.

3. Design a combinational circuit that compares two 4-bit numbers
A and B to check if they are equal. The circuit has one output X,
so that X = 1 if A = B and X = 0 if A is not equal to B.

4. A sequential circuit has three flip-flops, A, B, C; one input, X;
and one output, Y. The state diagram is shown below. The circuit is
to be designed by treating the unused states as don't-care conditions.
The final circuit must be self-correcting.

(a) use D flip-flops for the design
(b) use JK flip-flops for the design

5. Design a synchronous BCD counter using JK flip-flops. Determine the
next state for each of the six unused states.
Is your counter self-correcting or not ?